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Bol\\'ivar","submitted_at":"2011-06-18T03:42:57Z","abstract_excerpt":"We consider an initial value problem of type $$ \\frac{\\partial u}{\\partial t}={\\cal F}(t,x,u,\\partial_j u), \\quad u(0,x)=\\phi(x), $$ where $t$ is the time, $x \\in \\mathbb{R}^n $ and $u_0$ is a Clifford type algebra-valued function satisfying ${\\bf D}u=\\displaystyle\\sum_{j=0}^{n}\\lambda_j(x)e_j\\partial_ju = 0$, $\\lambda_j(x)\\in \\mathbb{R} $ for all $j$. We will solve this problem using the technique of associated spaces. In order to do that, we give sufficient conditions on the coefficients of the operators ${\\cal F}$ and ${\\bf D}$, where ${\\cal F}(u)= \\displaystyle\\sum_{i=0}^{n}A^{(i)}(x)\\disp"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1106.3611","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-06-18T03:42:57Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d3f13440dba6b3de08fe4ce3f183afbd73f22cad7f3460970aae796c7f1ad046","abstract_canon_sha256":"632f046bb01d319bc26b107b85611434e5512571a3283dd2875151bd74aa45d0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:42.689322Z","signature_b64":"DouRvqyw4N8o9BgqEvSAXcTimyP0EuBosFPm2f0QhX0Pi1QZuqrLHShHuRSCIw3XFqeGXxWlbVlaIx92cke2DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29c7aa68b56005cfeae95a10bb7f2e7103d0500581d9d7b5ab266594be3d6329","last_reissued_at":"2026-05-18T04:19:42.688760Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:42.688760Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Initial value problems in Clifford-type analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CV","authors_text":"Carmen J. Vanegas, Yanett M. Bol\\'ivar","submitted_at":"2011-06-18T03:42:57Z","abstract_excerpt":"We consider an initial value problem of type $$ \\frac{\\partial u}{\\partial t}={\\cal F}(t,x,u,\\partial_j u), \\quad u(0,x)=\\phi(x), $$ where $t$ is the time, $x \\in \\mathbb{R}^n $ and $u_0$ is a Clifford type algebra-valued function satisfying ${\\bf D}u=\\displaystyle\\sum_{j=0}^{n}\\lambda_j(x)e_j\\partial_ju = 0$, $\\lambda_j(x)\\in \\mathbb{R} $ for all $j$. We will solve this problem using the technique of associated spaces. 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